The generator matrix 1 0 0 0 1 1 1 1 0 1 1 1 X X X 1 1 1 1 1 0 X 0 1 1 1 1 0 0 X 1 1 0 X 0 1 0 1 1 1 1 1 1 X 1 1 0 X 1 X 1 X 0 X 1 1 1 1 1 1 1 0 1 0 0 1 0 0 1 1 0 1 1 1 1 0 0 X+1 X 1 0 1 0 X X X+1 X 1 1 X 1 1 1 1 1 1 X 1 X+1 X+1 1 0 0 0 1 1 0 1 1 1 X 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 1 1 0 0 1 1 0 0 0 X 1 0 1 0 X 1 1 X+1 X X 1 X X+1 X+1 1 X 0 0 0 X+1 1 0 X X+1 X+1 1 1 X+1 0 0 0 1 1 X 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0 1 1 0 1 X 0 1 X+1 X+1 0 1 1 X+1 1 0 X 1 1 1 0 0 X X 1 0 0 X 0 X 1 1 X 0 0 0 0 1 1 1 X 1 1 0 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 X X 0 X 0 0 0 X 0 X X 0 0 X X 0 X 0 0 0 0 X X X 0 X X X X 0 X 0 X X 0 0 0 0 X 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 X X X 0 0 X X X X 0 X 0 X 0 X X X X 0 X X 0 X 0 0 X 0 X 0 X X X 0 0 0 X X 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 X 0 X X X 0 X 0 X X 0 0 X X X 0 X 0 X X X 0 X 0 0 X X 0 X X X X 0 X 0 X 0 0 0 X X X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 X 0 X X 0 X X X 0 X X X 0 0 0 0 X 0 X X X 0 X 0 0 X X X 0 X 0 X X 0 X 0 0 0 X 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X 0 0 X 0 X 0 X X 0 0 0 X X 0 X 0 X X 0 X X 0 X X X 0 0 0 0 0 0 0 X X X 0 0 X X 0 0 X X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X 0 X X 0 X 0 0 X 0 0 X 0 0 X 0 X 0 X X 0 0 X X X 0 0 X 0 X X 0 X X 0 X 0 0 X X X 0 X X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X 0 0 0 0 X 0 X X X 0 X 0 0 0 X X 0 0 0 0 X X X 0 X X 0 X 0 0 X X X 0 0 X X X X X 0 0 0 0 0 0 0 generates a code of length 61 over Z2[X]/(X^2) who´s minimum homogenous weight is 40. Homogenous weight enumerator: w(x)=1x^0+68x^40+157x^42+321x^44+509x^46+72x^47+755x^48+140x^49+1020x^50+440x^51+1287x^52+688x^53+1302x^54+1458x^55+1091x^56+1764x^57+920x^58+2366x^59+746x^60+2500x^61+838x^62+2288x^63+892x^64+2100x^65+1058x^66+1172x^67+1238x^68+792x^69+1272x^70+338x^71+1116x^72+188x^73+787x^74+54x^75+517x^76+20x^77+261x^78+4x^79+135x^80+58x^82+19x^84+10x^86+5x^88+1x^96 The gray image is a linear code over GF(2) with n=122, k=15 and d=40. This code was found by Heurico 1.16 in 98 seconds.